Currently, there are a wide variety of devices that utilize optical circuits for communications and/or computations. Many optical circuits rely on one or more optical filter elements to filter out undesirable optical frequencies, so an optical frequency range of interest can be isolated.
In some applications, an MZI filter which can include a cascaded MZI filter, may demonstrate the theoretical capability of meeting the system specifications. However, when practical fabrication tolerances of the MZI filter are accounted for, the MZI filter may not be able to meet the system specifications without additional tuning. More specifically, an MZI filter employs two parallel waveguides and fabrication variations in the dimensions of the waveguides can produce undesirable shifts in the frequency response of the filter. This can lead to decreased performance parameters of the filter and/or, the failure to meet specifications and unacceptably high yield loss.
To compensate for fabrication variations some applications employ one or more heaters that are used to actively tune the filters using the thermo-optic effect in silicon. However, the use of heaters increases power consumption of the circuit and may not be effective for circuits that operate at cryogenic temperatures. Active tuning as a post-fabrication process is another common approach to mitigating fabrication variation, however active tuning can increase expense, may be dependent on foundry-specific processes, and could be intractable for circuits with numerous filters. Therefore, passive compensation structures for MZI filters that are intrinsically tolerant to perturbations from variations in waveguide dimensions and/or other ambient conditions are desired.